The sum of two numbers is 58. The larger number is 12 more than the smaller number . What are the numbers?

Question

The sum of two numbers is 58. The larger number is 12 more than the smaller number . What are the numbers?

Answer 1

The sum of two numbers = x + y=58

The larger number is 12 more than the smaller number= So, pick a letter, I choose X, Now add 12 to x.

You would write that as: x +12 and that is what you will replace the "y" with below.

So, y= x + 12, 

The replacement result would be:   x + x + 12=58 

X+X=2X or 2 times x 

So next just put that 2X into the equation like this: 2X + 12 = 58

Now Subtract 12 from BOTH sides of the equal sign.

What is left is 2X = 46

Because 2x is a multiplication problem, you must do the opposite to remove it by dividing both sides of the "=" by 2. 

So, 2/2=1 and any number times 1 is that original number. So will just write X

Therefore that leaves X by itself on the left side of the = sign. And now divide 46/2= 23

So, x=46/2

The result is x=23.

We know the larger number or "y" is 12 more than x (the smaller number). So Replace X with 23 and you get:

y=23 + 12 = 35 Therefore y= 35

Ok So x= 23 and Y = 35

The numbers are 23 and 35. 

 

Answer 2

Say the two numbers are represented by : x and y

That says x+y= 58

Let us say that x is the larger number, and it is 12 more than the smaller number y; set it up as below,

x=12+y

Now we have two equations and two unknowns, solve for x and y. With some algebra, we get

 

x=35, y=23.

 

As you can see x is larger than y by 12, and the sum is 58.

If you have difficulty solving for x and y, I can help with that.